This paper reports on variants of the Square attack applied to
reduced-round versions of the PES and IDEA block ciphers. Attacks
on 2.5 rounds of IDEA require $3\cdot 2^{16}$ chosen-plaintexts and
recover 78 key bits. A new kind of attack, the Square
related-key attack, is applied on 2.5 rounds of IDEA and recovers
32 key bits, with 2 chosen-plaintexts and $2^{17}$
related keys. Similar results hold for 2.5 rounds of PES.
Implementations of the attacks on 32-bit block mini-versions of both
ciphers confirmed the expected computational complexity. Although
our attacks do not improve on previous approaches, this report shows
new variants of the Square attack on word-oriented block ciphers
like IDEA and PES.